यदि (p(x)=2x-2 +bx+c), (p(0)=5) और (p(1)=1), तो (b) क्या है?
If (p(x)=2x-2 +bx+c), (p(0)=5), and (p(1)=1), what is (b)?
#parameter
#constant term
#evaluation
A (-6)
B (-5)
C (-4)
D (-3)
Explanation opens after your attempt
Step 1
Concept
(p(0)=c=5) and (p(1)=2+b+5=1), so (b=-6). The constant term is found quickly from (x=0).
Step 2
Why this answer is correct
The correct answer is A. (-6). (p(0)=c=5) and (p(1)=2+b+5=1), so (b=-6). The constant term is found quickly from (x=0).
Step 3
Exam Tip
(p(0)=c=5) और (p(1)=2+b+5=1), इसलिए (b=-6)। (x=0) से अचर पद तुरंत मिलता है।
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किस मान के लिए ((m+1)x-2 +(m-2 )x+7) अचर बहुपद बन सकता है?
For what value of (m) can ((m+1)x-2 +(m-2 )x+7) become a constant polynomial?
#constant polynomial
#parameter
#condition
A (m=-1)
B (m=2)
C ऐसा कोई मान नहीं / No such value
D (m=1)
Explanation opens after your attempt
Correct Answer
C. ऐसा कोई मान नहीं / No such value
Step 1
Concept
For a constant polynomial, both (m+1=0) and (m-2 =0) are needed, which is impossible together. All variable terms must vanish.
Step 2
Why this answer is correct
The correct answer is C. ऐसा कोई मान नहीं / No such value. For a constant polynomial, both (m+1=0) and (m-2 =0) are needed, which is impossible together. All variable terms must vanish.
Step 3
Exam Tip
अचर बहुपद के लिए (m+1=0) और (m-2 =0) दोनों चाहिए, जो साथ संभव नहीं हैं। सभी चर वाले पद हटने चाहिए।
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यदि (p(x)=x-3 +rx-2 +s), (p(0)=5) और (p(1)=9), तो (r) क्या है?
If (p(x)=x-3 +rx-2 +s), (p(0)=5), and (p(1)=9), what is (r)?
#parameter
#evaluation
#cubic
A (1)
B (2)
C (3)
D (4)
Explanation opens after your attempt
Step 1
Concept
(p(0)=s=5) and (p(1)=1+r+5=9), so (r=3). First use (x=0) to find the constant term.
Step 2
Why this answer is correct
The correct answer is C. (3). (p(0)=s=5) and (p(1)=1+r+5=9), so (r=3). First use (x=0) to find the constant term.
Step 3
Exam Tip
(p(0)=s=5) और (p(1)=1+r+5=9), इसलिए (r=3)। पहले (x=0) से अचर पद निकालें।
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यदि (p(x)=x-3 +px+q), (p(1)=4) और (p(-1)=-2), तो (p) का मान क्या है?
If (p(x)=x-3 +px+q), (p(1)=4), and (p(-1)=-2), what is the value of (p)?
#parameter
#cubic
#evaluation
A (1)
B (2)
C (3)
D (4)
Explanation opens after your attempt
Step 1
Concept
The conditions give (1+p+q=4) and (-1-p+q=-2), so (p=2). Subtracting the two equations is quick.
Step 2
Why this answer is correct
The correct answer is B. (2). The conditions give (1+p+q=4) and (-1-p+q=-2), so (p=2). Subtracting the two equations is quick.
Step 3
Exam Tip
शर्तों से (1+p+q=4) और (-1-p+q=-2), इसलिए (p=2)। दो समीकरणों को घटाना तेज तरीका है।
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यदि बहुपद (p(x)=2x-3 +kx-2 -8x+3) में सभी गुणांकों का योग (0) है, तो (k) क्या है?
If the sum of all coefficients of (p(x)=2x-3 +kx-2 -8x+3) is (0), what is (k)?
#sum of coefficients
#parameter
#polynomial
A (1)
B (2)
C (3)
D (4)
Explanation opens after your attempt
Step 1
Concept
The sum of coefficients is (2+k-8+3=k-3), so (k=3). The sum of coefficients can also be found by (p(1)).
Step 2
Why this answer is correct
The correct answer is C. (3). The sum of coefficients is (2+k-8+3=k-3), so (k=3). The sum of coefficients can also be found by (p(1)).
Step 3
Exam Tip
गुणांकों का योग (2+k-8+3=k-3) है, इसलिए (k=3)। गुणांकों का योग (p(1)) से भी मिलता है।
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यदि (p(x)=x-2 +ax+b), (p(1)=0) और (p(2)=0), तो (a+b) क्या है?
If (p(x)=x-2 +ax+b), (p(1)=0), and (p(2)=0), what is (a+b)?
#simultaneous equations
#zeros
#parameter
A (-1)
B (0)
C (1)
D (2)
Explanation opens after your attempt
Step 1
Concept
The conditions give (1+a+b=0) and (4+2a+b=0), so (a=-3), (b=2), and (a+b=-1). The correct option is (-1).
Step 2
Why this answer is correct
The correct answer is C. (1). The conditions give (1+a+b=0) and (4+2a+b=0), so (a=-3), (b=2), and (a+b=-1). The correct option is (-1).
Step 3
Exam Tip
शर्तों से (1+a+b=0) और (4+2a+b=0), इसलिए (a=-3), (b=2) और (a+b=-1)। सही विकल्प (-1) है।
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किस मान के लिए (p(x)=x-3 -4x-2 +mx+6) में (p(1)=0) होगा?
For what value of (m) will (p(1)=0) in (p(x)=x-3 -4x-2 +mx+6)?
#parameter
#evaluation
#cubic
A (-3)
B (-2)
C (2)
D (3)
Explanation opens after your attempt
Step 1
Concept
(p(1)=1-4+m+6=m+3), so (m=-3). Substitute the given value and form a simple equation.
Step 2
Why this answer is correct
The correct answer is A. (-3). (p(1)=1-4+m+6=m+3), so (m=-3). Substitute the given value and form a simple equation.
Step 3
Exam Tip
(p(1)=1-4+m+6=m+3), इसलिए (m=-3)। दिए गए मान को रखकर सरल समीकरण बनाएं।
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यदि (x=3), बहुपद (p(x)=x-2 -kx+12) का शून्य है, तो (k) क्या है?
If (x=3) is a zero of (p(x)=x-2 -kx+12), what is (k)?
#zero
#parameter
#quadratic
A (5)
B (6)
C (7)
D (8)
Explanation opens after your attempt
Step 1
Concept
(p(3)=9-3k+12=0), so (21=3k) and (k=7). For a zero, set the polynomial value equal to (0).
Step 2
Why this answer is correct
The correct answer is C. (7). (p(3)=9-3k+12=0), so (21=3k) and (k=7). For a zero, set the polynomial value equal to (0).
Step 3
Exam Tip
(p(3)=9-3k+12=0), इसलिए (21=3k) और (k=7)। शून्य की शर्त में बहुपद का मान (0) रखें।
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यदि (p(x)=kx-2 -5x+6) और (p(-1)=14), तो (k) का मान क्या है?
If (p(x)=kx-2 -5x+6) and (p(-1)=14), what is the value of (k)?
#evaluation
#parameter
#polynomial
A (1)
B (2)
C (3)
D (4)
Explanation opens after your attempt
Step 1
Concept
(p(-1)=k+5+6=14), so (k=3). Check signs carefully while substituting a negative value.
Step 2
Why this answer is correct
The correct answer is C. (3). (p(-1)=k+5+6=14), so (k=3). Check signs carefully while substituting a negative value.
Step 3
Exam Tip
(p(-1)=k+5+6=14), इसलिए (k=3)। ऋणात्मक मान रखते समय संकेत सावधानी से देखें।
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यदि (p(x)=(a-5)x-5 +2x-3 -7x+4) की घात (3) है, तो (a) क्या होगा?
If the degree of (p(x)=(a-5)x-5 +2x-3 -7x+4) is (3), what is (a)?
#degree
#parameter
#polynomial
A (0)
B (3)
C (5)
D (7)
Explanation opens after your attempt
Step 1
Concept
For the degree to be (3), the coefficient of \(x^5\) must be (0), so (a-5=0). First make the highest-degree term vanish.
Step 2
Why this answer is correct
The correct answer is C. (5). For the degree to be (3), the coefficient of \(x^5\) must be (0), so (a-5=0). First make the highest-degree term vanish.
Step 3
Exam Tip
घात (3) होने के लिए \(x^5\) का गुणांक (0) होना चाहिए, इसलिए (a-5=0)। उच्चतम घात वाले पद को पहले शून्य करें।
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यदि (p(x)=ax-2 +4x-12) और (x=2) इसका शून्य है, तो (a) क्या होगा?
If (p(x)=ax-2 +4x-12) and (x=2) is its zero, what is (a)?
#zero condition
#parameter
#quadratic
A (1)
B (2)
C (3)
D (4)
Explanation opens after your attempt
Step 1
Concept
(p(2)=4a+8-12=0), so (4a=4) and (a=1). When a zero is given, set the polynomial value equal to (0).
Step 2
Why this answer is correct
The correct answer is A. (1). (p(2)=4a+8-12=0), so (4a=4) and (a=1). When a zero is given, set the polynomial value equal to (0).
Step 3
Exam Tip
(p(2)=4a+8-12=0), इसलिए (4a=4) और (a=1)। शून्य दिए होने पर बहुपद का मान (0) रखें।
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यदि (p(x)=2x-2 -5x+c) और (p(4)=7), तो (c) का मान क्या है?
If (p(x)=2x-2 -5x+c) and (p(4)=7), what is the value of (c)?
#evaluation
#parameter
#constant term
A (-5)
B (-3)
C (3)
D (5)
Explanation opens after your attempt
Step 1
Concept
(p(4)=32-20+c=7), so (12+c=7) and (c=-5). Substitute the given value to find the unknown constant term.
Step 2
Why this answer is correct
The correct answer is A. (-5). (p(4)=32-20+c=7), so (12+c=7) and (c=-5). Substitute the given value to find the unknown constant term.
Step 3
Exam Tip
(p(4)=32-20+c=7), इसलिए (12+c=7) और (c=-5)। दिए गए मान को रखकर अज्ञात अचर पद निकालें।
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यदि (p(x)=(k-4)x-4 +3x-2 -5x+2) की घात (2) है, तो (k) का मान क्या होगा?
If the degree of (p(x)=(k-4)x-4 +3x-2 -5x+2) is (2), what will be the value of (k)?
#degree
#parameter
#polynomial
A (0)
B (2)
C (4)
D (6)
Explanation opens after your attempt
Step 1
Concept
For the degree to be (2), the coefficient of \(x^4\) must be (0), so (k-4=0) and (k=4). Check the coefficient of the highest power first.
Step 2
Why this answer is correct
The correct answer is C. (4). For the degree to be (2), the coefficient of \(x^4\) must be (0), so (k-4=0) and (k=4). Check the coefficient of the highest power first.
Step 3
Exam Tip
घात (2) होने के लिए \(x^4\) का गुणांक (0) होना चाहिए, इसलिए (k-4=0) और (k=4)। सबसे बड़ी घात वाले पद का गुणांक पहले जांचें।
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यदि (p(x)=ax-3 +bx-2 +cx+d) और (p(0)=-7), तो (d) का मान क्या है?
If (p(x)=ax-3 +bx-2 +cx+d) and (p(0)=-7), what is the value of (d)?
#polynomial-value
#constant-term
#parameter
A (7)
B (-7)
C (0)
D (a+b+c)
Explanation opens after your attempt
Step 1
Concept
Putting (x=0) gives (p(0)=d). Therefore (d=-7).
Step 2
Why this answer is correct
The correct answer is B. (-7). Putting (x=0) gives (p(0)=d). Therefore (d=-7).
Step 3
Exam Tip
(x=0) रखने पर (p(0)=d) मिलता है। इसलिए (d=-7) है।
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किस मान के लिए \(x^2-6x+m\) में (x=2) शून्य होगा?
For what value of (m) will (x=2) be a zero of \(x^2-6x+m\)?
#zero
#parameter
#quadratic
A (6)
B (8)
C (10)
D (12)
Explanation opens after your attempt
Step 1
Concept
(4-12+m=0), so (m=8). When a zero is given, set the polynomial value equal to (0).
Step 2
Why this answer is correct
The correct answer is B. (8). (4-12+m=0), so (m=8). When a zero is given, set the polynomial value equal to (0).
Step 3
Exam Tip
(4-12+m=0), इसलिए (m=8)। शून्य दिए होने पर बहुपद का मान (0) रखें।
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यदि (p(x)=x-2 -ax+18) और (p(3)=0), तो (a) का मान क्या है?
If (p(x)=x-2 -ax+18) and (p(3)=0), what is the value of (a)?
#parameter
#evaluation
#quadratic polynomial
A (7)
B (8)
C (9)
D (10)
Explanation opens after your attempt
Step 1
Concept
(p(3)=9-3a+18=0), so (27=3a) and (a=9). After substitution, solve the simple linear equation.
Step 2
Why this answer is correct
The correct answer is C. (9). (p(3)=9-3a+18=0), so (27=3a) and (a=9). After substitution, solve the simple linear equation.
Step 3
Exam Tip
(p(3)=9-3a+18=0), इसलिए (27=3a) और (a=9)। मान रखने के बाद सरल रैखिक समीकरण हल करें।
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यदि (p(x)=x-2 +kx-15) और (p(3)=0), तो (k) क्या है?
If (p(x)=x-2 +kx-15) and (p(3)=0), what is (k)?
#parameter
#zero condition
#quadratic
A (2)
B (3)
C (4)
D (5)
Explanation opens after your attempt
Step 1
Concept
(p(3)=9+3k-15=0), so (3k=6) and (k=2). Use the zero condition to find the unknown.
Step 2
Why this answer is correct
The correct answer is A. (2). (p(3)=9+3k-15=0), so (3k=6) and (k=2). Use the zero condition to find the unknown.
Step 3
Exam Tip
(p(3)=9+3k-15=0), इसलिए (3k=6) और (k=2)। शून्य की शर्त लगाकर अज्ञात निकालें।
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यदि (p(x)=9x-2 +cx-5) में (x) का गुणांक (-4) है, तो (c) क्या है?
If the coefficient of (x) in (p(x)=9x-2 +cx-5) is (-4), what is (c)?
#coefficient
#parameter
#polynomial
A (-9)
B (-5)
C (-4)
D (4)
Explanation opens after your attempt
Step 1
Concept
In (cx), the coefficient of (x) is (c). It is given that (c=-4).
Step 2
Why this answer is correct
The correct answer is C. (-4). In (cx), the coefficient of (x) is (c). It is given that (c=-4).
Step 3
Exam Tip
(cx) में (x) का गुणांक (c) है। दिया है कि (c=-4)।
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यदि (p(x)=(a+3)x-2 +5x-1) रैखिक बहुपद है, तो (a) क्या होगा?
If (p(x)=(a+3)x-2 +5x-1) is a linear polynomial, what is (a)?
#linear condition
#parameter
#degree
A (-3)
B (0)
C (3)
D (5)
Explanation opens after your attempt
Step 1
Concept
For it to be linear, the coefficient of \(x^2\) must be (0). Hence (a+3=0) and (a=-3).
Step 2
Why this answer is correct
The correct answer is A. (-3). For it to be linear, the coefficient of \(x^2\) must be (0). Hence (a+3=0) and (a=-3).
Step 3
Exam Tip
रैखिक होने के लिए \(x^2\) का गुणांक (0) होना चाहिए। इसलिए (a+3=0) और (a=-3)।
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यदि (p(x)=x-2 -ax+12) और (p(3)=0), तो (a) का मान क्या है?
If (p(x)=x-2 -ax+12) and (p(3)=0), what is the value of (a)?
#parameter
#zero
#quadratic
A (5)
B (6)
C (7)
D (8)
Explanation opens after your attempt
Step 1
Concept
(9-3a+12=0) gives (21-3a=0). Therefore (a=7).
Step 2
Why this answer is correct
The correct answer is C. (7). (9-3a+12=0) gives (21-3a=0). Therefore (a=7).
Step 3
Exam Tip
(9-3a+12=0) से (21-3a=0) मिलता है। इसलिए (a=7) है।
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यदि (p(x)=x-2 +px+16) और (4) इसका शून्य है, तो (p) का मान क्या है?
If (4) is a zero of (p(x)=x-2 +px+16), what is the value of (p)?
#zero
#parameter
#quadratic
A (-8)
B (-4)
C (4)
D (8)
Explanation opens after your attempt
Step 1
Concept
\(4^2+4p+16=0\) gives (32+4p=0). Therefore (p=-8).
Step 2
Why this answer is correct
The correct answer is A. (-8). \(4^2+4p+16=0\) gives (32+4p=0). Therefore (p=-8).
Step 3
Exam Tip
\(4^2+4p+16=0\) से (32+4p=0) मिलता है। इसलिए (p=-8) है।
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यदि (p(x)=2x-2 +bx-10) और (p(2)=4), तो (b) का मान क्या है?
If (p(x)=2x-2 +bx-10) and (p(2)=4), what is the value of (b)?
#parameter
#polynomial-value
#linear-equation
A (1)
B (2)
C (3)
D (4)
Explanation opens after your attempt
Step 1
Concept
(p(2)=8+2b-10=4) gives (2b-2=4). Therefore (b=3).
Step 2
Why this answer is correct
The correct answer is C. (3). (p(2)=8+2b-10=4) gives (2b-2=4). Therefore (b=3).
Step 3
Exam Tip
(p(2)=8+2b-10=4) से (2b-2=4) मिलता है। इसलिए (b=3) है।
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यदि (p(x)=x-3 +ax-2 +bx+1) में (a=0) और (b=-2), तो बहुपद क्या होगा?
If (a=0) and (b=-2) in (p(x)=x-3 +ax-2 +bx+1), what will the polynomial be?
#parameter
#substitution
#polynomial-form
A \(x^3-2x+1\)
B \(x^3+2x+1\)
C \(x^3-2x^2+1\)
D \(x^3+x^2-2x\)
Explanation opens after your attempt
Correct Answer
A. \(x^3-2x+1\)
Step 1
Concept
With (a=0), the \(x^2\) term vanishes, and with (b=-2), we get (-2x). So the polynomial is \(x^3-2x+1\).
Step 2
Why this answer is correct
The correct answer is A. \(x^3-2x+1\). With (a=0), the \(x^2\) term vanishes, and with (b=-2), we get (-2x). So the polynomial is \(x^3-2x+1\).
Step 3
Exam Tip
(a=0) से \(x^2\) पद हटता है और (b=-2) से (-2x) मिलता है। इसलिए बहुपद \(x^3-2x+1\) है।
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यदि \(x^3+2x^2+cx+5\) में (x) का गुणांक (6) है, तो (c+5) क्या होगा?
If the coefficient of (x) in \(x^3+2x^2+cx+5\) is (6), what will be (c+5)?
#coefficient
#parameter
#evaluation
A (6)
B (9)
C (11)
D (15)
Explanation opens after your attempt
Step 1
Concept
The coefficient of (x) is (c=6). Therefore (c+5=11).
Step 2
Why this answer is correct
The correct answer is C. (11). The coefficient of (x) is (c=6). Therefore (c+5=11).
Step 3
Exam Tip
(x) का गुणांक (c=6) है। इसलिए (c+5=11) होगा।
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यदि (p(x)=x-2 +ax+a) और (p(1)=5), तो (a) का मान क्या है?
If (p(x)=x-2 +ax+a) and (p(1)=5), what is the value of (a)?
#parameter
#polynomial-value
#substitution
A (1)
B (2)
C (3)
D (4)
Explanation opens after your attempt
Step 1
Concept
(p(1)=1+a+a=5) gives (1+2a=5). Therefore (a=2).
Step 2
Why this answer is correct
The correct answer is B. (2). (p(1)=1+a+a=5) gives (1+2a=5). Therefore (a=2).
Step 3
Exam Tip
(p(1)=1+a+a=5) से (1+2a=5) मिलता है। इसलिए (a=2) है।
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यदि (p(x)=kx+12) का शून्य (3) है, तो (k) का मान क्या है?
If (3) is a zero of (p(x)=kx+12), what is the value of (k)?
#linear-polynomial
#zero
#parameter
A (4)
B (-4)
C (9)
D (-9)
Explanation opens after your attempt
Step 1
Concept
From (p(3)=0), we get (3k+12=0). Therefore (k=-4).
Step 2
Why this answer is correct
The correct answer is B. (-4). From (p(3)=0), we get (3k+12=0). Therefore (k=-4).
Step 3
Exam Tip
(p(3)=0) से (3k+12=0) मिलता है। इसलिए (k=-4) है।
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किस मान के लिए (p(x)=(a-2)x-3 +4x-2 +1) की घात (2) हो जाएगी?
For which value will (p(x)=(a-2)x-3 +4x-2 +1) have degree (2)?
#degree
#parameter
#highest-power
A (a=0)
B (a=1)
C (a=2)
D (a=4)
Explanation opens after your attempt
Step 1
Concept
For degree (2), the coefficient of \(x^3\) must be (0). From (a-2=0), we get (a=2).
Step 2
Why this answer is correct
The correct answer is C. (a=2). For degree (2), the coefficient of \(x^3\) must be (0). From (a-2=0), we get (a=2).
Step 3
Exam Tip
घात (2) के लिए \(x^3\) का गुणांक (0) होना चाहिए। (a-2=0) से (a=2) मिलता है।
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यदि (p(x)=2x-3 +mx-2 -x+4) में \(x^2\) का गुणांक (-5) है, तो (m) क्या है?
If the coefficient of \(x^2\) in (p(x)=2x-3 +mx-2 -x+4) is (-5), what is (m)?
#coefficient
#parameter
#polynomial
A (5)
B (-5)
C (2)
D (-1)
Explanation opens after your attempt
Step 1
Concept
The multiplier of \(x^2\) is (m). Given (m=-5), so the answer is (-5).
Step 2
Why this answer is correct
The correct answer is B. (-5). The multiplier of \(x^2\) is (m). Given (m=-5), so the answer is (-5).
Step 3
Exam Tip
\(x^2\) के साथ लगा गुणक (m) है। दिया है (m=-5), इसलिए उत्तर (-5) है।
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यदि (q(x)=x-2 -kx+6) और (q(2)=0), तो (k) का मान क्या है?
If (q(x)=x-2 -kx+6) and (q(2)=0), what is the value of (k)?
#zero-of-polynomial
#parameter
#substitution
A (3)
B (4)
C (5)
D (6)
Explanation opens after your attempt
Step 1
Concept
(q(2)=4-2k+6=0) gives (10-2k=0). So (k=5).
Step 2
Why this answer is correct
The correct answer is C. (5). (q(2)=4-2k+6=0) gives (10-2k=0). So (k=5).
Step 3
Exam Tip
(q(2)=4-2k+6=0) से (10-2k=0) मिलता है। इसलिए (k=5) है।
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यदि (p(x)=ax-2 +3x+5) की घात (1) है, तो (a) का मान क्या होगा?
If (p(x)=ax-2 +3x+5) has degree (1), what will be the value of (a)?
#polynomials
#degree
#parameter
A (0)
B (1)
C (3)
D (5)
Explanation opens after your attempt
Step 1
Concept
For degree (1), the coefficient of \(x^2\) must be (0). Therefore (a=0).
Step 2
Why this answer is correct
The correct answer is A. (0). For degree (1), the coefficient of \(x^2\) must be (0). Therefore (a=0).
Step 3
Exam Tip
घात (1) होने के लिए \(x^2\) का गुणांक (0) होना चाहिए। इसलिए (a=0) है।
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